Logarithms have the property that log(a)-log(b)=log(a/b) if they have the same base. So you do this to combine the logs, next you undo the logs by raising the base of the log to the power of both each side i.e. if log(a/b)=c where c is a constant then a/b=k^c where k is the base of the log. After this it is a matter of algebra.

When you switch the y and the x cooridinates to find a solution by graphing, solve for y. Or in other words, find the inverse of the function, and before you do that find out if the function is one-to-one.